Given that \(f(x)=x^{2}-px+q\) has has two prime numbers as roots and \(p+q=11\) where \(p\) is an odd positive integer.

\[f(1)+f(2)+f(3)+f(4)+\cdots+f(48)\]

If the value of the above expression is \(A\), then find \(\dfrac{A}{16}-11\).

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